It is known that a tracing milling machine can be used for machining a metallic product having a shape so complicated that the dimensional indication of the shape by the use of a design drawing or drawings is impossible. For instance, a conventional tracking milling machine is widely used for machining male and female metal products. The tracing milling machine is always provided with a tracer head to which a tracer with a stylus is attached. The tracer performs a tracing movement over the surface of a template or a model, and in response to the tracing movement of the tracer, the movement of a cutting tool for carrying out the machining of the metal product from a workpiece is servo-controlled. The tracing movement of the tracer can be performed in diverse ways or modes such as, for example, a both way tracing mode, a one way scan tracing mode, a partial contour tracing mode, a 360.degree. contour tracing mode, or a three dimensional tracing mode. However, in a conventional tracing milling machine, automation of the entire machining process of a product is incomplete. Therefore, the control of the continuous diverse tracing milling processes as well as the selection and setting of the diverse tracking modes must be carried out by employing an operating panel by which a human operator operates the tracing milling machine. Further, mechanical dog members must be employed for limiting the tracing movement of the tracer. As a result, one human operator is always needed for operating one conventional tracing milling machine. Accordingly, it is apparent that the degree of automation of the conventional tracing milling machine is incomplete as compared with that of a conventional numerically controlled machine tool or a conventional fully automated machining center. Also, with the conventional tracing milling machine, it is well known that the machining of a metal mold having a complicated male or female shape requires a long machining time, since the machining of a metal mold from a raw workpiece must undergo many processes, such as rough, intermediate and finish machining processes. Accordingly, during the entire machining process of a metal mold from a raw workpiece thereof, it is always necessary to replace the used cutting tool attached to the spindle head of the conventional tracing milling machine with a fresh cutting tool. Further, when a cutting tool attached to the spindle head is worn or broken, such worn or broken cutting tool must be replaced with a fresh cutting tool. Therefore, the demand for a so-called automatic tool changer for a tracing milling machine is increasing, since no conventional tracing milling machine is provided with an automatic tool changer. Moreover, it is obvious that if a tracing milling machine is provided with an automatic tool changer, and if the automatic tool change is appropriately performed during the rough and finish machining processes of a metal product, the efficiency of the entire tracing milling process of the metal product will be enhanced. In this regard, however, it should be noted that a tracing milling machine must also be provided with an appropriate means for automatically detecting the need for replacing a used cutting tool attached to the spindle head of the tracing milling machine with a fresh cutting tool stored in the automatic tool changer.